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Importance of the geometry of twisted yarns


The translation of the physical properties of textile fibers into textile structures, such as yarns and fabrics is a function of both the fiber properties and the geometric configuration they assume in the ultimate end product. Earlier studies of the relationship between yarn structure and properties have been along empirical or semi-empirical lines. However, many technologists who are concerned with the evaluation of the physical properties of textile structures have realized that these relationships are governed by same physical and engineering concepts as those e\used so successfully in the characterization of more classic structural materials such as steel and concrete. Hearle and Backer have given an excellent account of the progressive development of the ideas in this field of study. Nevertheless, it is considered appropriate to consider some basic concepts that are relevant to the study of yarn structure and properties. One such aspect is the understanding of the geometry of twisted yarns that is so vital in analyzing the stress-strain behavior of yarns in addition to various other physical properties.

GEOMETRY OF THE IDEALIZED TWISTED YARNS:
In the definition of the geometry of the single yarn the model is usually adopted as an ideal physical form. This is a coaxial helix model as illustrated in Fig. 5.5. of Goswami. The assumptions underlying the model are characterized by the following assumptions:-
1)      The yarn is circular in cross-section and is uniform along its length.
2)      It is built-up of a series of superimposed concentric layers of different radii in each of which the fibers follow a uniform helical path so that its distance from the centre remains constant.
3)      A filament at the centre will follow the straight line of the yarn axis, but going out from the centre the helix angle gradually increases, since the twist per unit length in all the layers remains constant.
4)      The axis of the circular cylinders coincides with the yarn axis.
5)      The number of filaments of fibers crossing the unit area is constant throughout the model.
6)      The structure is assumed to be made up of a large number of filaments: this will avoid any complications arising because of any discrepancies in packing of fibers. There are two types of packing, I) open packing where the fibers are in loose position, and ii) close packing where the fibers are very compact.
The idealized model can be used to derive some very useful geometrical relations related to its various physical properties. The parameters involved in characterizing the idealized geometry are:

R= Yarn radius (cm).
r = Radius of the cylinder containing the helical path of a particular fiber(cm).
T = Yarn twist, (turns per unit length ( cm  ).
h = Length of one turn of twist (cm).
α = Surface angle of twist (the angle between the axis of a fiber on the surface and a line
      parallel to the yarn axis (degrees).
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